The book is divided into four chapters that are designed to engage readers in the study of calculus. Throughout the chapters, each of the studies is corroborated by many examples, solved problems, and proposed problems. Full and detailed solutions are provided for all problems included in the book. The first chapter is dedicated to the study of real numbers. In particular, the reader encounters the axioms of real numbers and the notion of rationality versus irrationality, while exploring interesting consequences of the density of the rational numbers. In the second chapter the focus shifts to sequences of real numbers, examining convergent and divergent sequences, working with limits, and understanding their profound implications. The third chapter explores series and infinite products. Starting with some fundamentals and elementary convergence tests, the concepts of absolute con-vergence and conditional convergence are showcased. The last chapter proposes a problem set drawn from different areas of mathematics unified by the application of the knowledge acquired in the previous chapters.
Authors
- Titu Andreescu and Alessandro Ventullo
Subjects
- Mixed Topics
Book Details
- Hardcover: 360 pages
- Publisher: XYZ Press (2024)
- Language: English
- ISBN-13: 979-8-9890528-8-2
